Selective final state spectroscopy and multifractality in two-component ultracold Bose-Einstein condensates: a numerical study

TL;DR

This study proposes a numerical method to observe multifractality at the mobility edge in ultracold Bose-Einstein condensates using state-dependent disordered potentials and advanced imaging techniques.

Contribution

It introduces a novel approach combining radio frequency pulses and laser microscopy to detect critical multifractal states near the Anderson localization transition.

Findings

Multifractality can be observed in the density distributions of ultracold bosons.

Universal density correlations emerge at the mobility edge.

Interference fringes reveal localized phase properties.

Abstract

We propose to use the method introduced by Volchkov et al., based on state dependent disordered ultracold bosons, to address the critical state at the mobility edge of the Anderson localization transition, and to observe its intriguing multifractal structure. An optimally designed external radio frequency pulse can be applied to generate transitions to eigenstates in a narrow energy window close to the mobility edge, where critical scaling and multifractality emerge. Two-photon laser scanning microscopy will be used to address individual localized states even close to the transition. The projected image of the cloud is shown to inherit multifractality and to display universal density correlations. Time of flight images of the excited states are predicted to show interference fringes in the localized phase, while they allow one to map equal energy surfaces deep in the metallic phase.